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A Lagrangian function is constructed to combine the objective and multiple equality constraints.
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With regard to the design problem of compliant mechanisms subject to multiple equality displacement constraints and an area constraint, we here present a unified sensitivity analysis procedure based on artificial reaction forces, in which the key idea is built upon the Lagrange multiplier method.
Absolute equality constraints in multiple regression are shown to introduce only minor modifications in the normal equations by a subset of the regression parameters.
Basically, it determines the top and bottom depths for multiple rectangular prisms using inequality or equality constraints for those depths.
The equality constraints are removed.
As such all equality constraints are satisfied.
denotes the number of equality constraints.
These properties might be expressed using equality constraints, inequality constraints or membership constraints.
A new dynamic tolerance technique to handle equality constraints is also adopted.
The numerical technique of differential quadrature (DQ) is adopted to approximate these DAEs with equality constraints.
As the equality constraints, the volume of material and the capacity of a shell are considered.
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